Schmid left the game with 9 1/2 minutes left after absorbing a hard hit that was ruled as targeting. He returned to finish the drive with Ramon Jefferson running in from 5 yards out and Schmid throwing for the two-point conversion and a 42-28 lead.
Schmid threw all of his touchdown passes in the first half, including a 45-yarder to Jequez Ezzard to open the scoring, as the Bearkats took off to a 31-7 lead.
Breylin Smith's 5-yard TD pass to Tyler Hudson with nine seconds left in the half cut the lead to 31-14.
Central Arkansas, ranked 24th in the coaches poll, cut into the leader further with Smith's 24-yard pass to Lujuan Winningham and Darius Hale's 7-yard run in the third quarter to trail 31-28.
The Bearkats (3-0) outgained the Bears (1-3) 478-326 in winning their 14th straight.
Schmid was 19-of-37 passing for 283 yards. Two of his TD passes went to Ezzard. Jefferson rushed for 104 yards on 22 carries.
Smith was 25 of 41 for 288 yards passing, four touchdowns and two interceptions. Hudson had 11 catches for a career-high 181 yards and two TDs.
The game was the first for both teams within the Atlantic Sun-Western Athletic Conference Challenge. Seven teams are playing in the Challenge, also being called the AQ7, in which designated teams from the two conferences will play a single round-robin. The team with the highest winning percentage out of the Challenge will get the automatic bid to the FCS playoffs.
More AP college football: https://apnews.com/hub/college-football and https://twitter.com/AP-Top25.
Sign up for the AP's college football newsletter: https://apnews.com/cfbtop25
Copyright 2021 STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.